Combinatorics of Second Derivative: Graphical Proof of Glaisher-Crofton Identity
We give a purely combinatorial proof of the Glaisher-Crofton identity which is derived from the analysis of discrete structures generated by the iterated action of the second derivative. The argument illustrates the utility of symbolic and generating function methodology of modern enumerative combin...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/9575626 |
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| author | Pawel Blasiak Gérard H. E. Duchamp Karol A. Penson |
| author_facet | Pawel Blasiak Gérard H. E. Duchamp Karol A. Penson |
| author_sort | Pawel Blasiak |
| collection | DOAJ |
| description | We give a purely combinatorial proof of the Glaisher-Crofton identity which is derived from the analysis of discrete structures generated by the iterated action of the second derivative. The argument illustrates the utility of symbolic and generating function methodology of modern enumerative combinatorics. The paper is meant for nonspecialists as a gentle introduction to the field of graphical calculus and its applications in computational problems. |
| format | Article |
| id | doaj-art-7c3ee449d9f84c59b7618b2bf9e91ebd |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-7c3ee449d9f84c59b7618b2bf9e91ebd2025-02-03T05:52:46ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/95756269575626Combinatorics of Second Derivative: Graphical Proof of Glaisher-Crofton IdentityPawel Blasiak0Gérard H. E. Duchamp1Karol A. Penson2Institute of Nuclear Physics Polish Academy of Sciences, 31342 Kraków, PolandUniversité Paris 13, Sorbonne Paris Cité, LIPN, CNRS UMR 7030, 93430 Villetaneuse, FranceUniversité Pierre et Marie Curie (Paris 06), Sorbonne Universités, LPTMC, CNRS UMR 7600, 75252 Paris Cedex 05, FranceWe give a purely combinatorial proof of the Glaisher-Crofton identity which is derived from the analysis of discrete structures generated by the iterated action of the second derivative. The argument illustrates the utility of symbolic and generating function methodology of modern enumerative combinatorics. The paper is meant for nonspecialists as a gentle introduction to the field of graphical calculus and its applications in computational problems.http://dx.doi.org/10.1155/2018/9575626 |
| spellingShingle | Pawel Blasiak Gérard H. E. Duchamp Karol A. Penson Combinatorics of Second Derivative: Graphical Proof of Glaisher-Crofton Identity Advances in Mathematical Physics |
| title | Combinatorics of Second Derivative: Graphical Proof of Glaisher-Crofton Identity |
| title_full | Combinatorics of Second Derivative: Graphical Proof of Glaisher-Crofton Identity |
| title_fullStr | Combinatorics of Second Derivative: Graphical Proof of Glaisher-Crofton Identity |
| title_full_unstemmed | Combinatorics of Second Derivative: Graphical Proof of Glaisher-Crofton Identity |
| title_short | Combinatorics of Second Derivative: Graphical Proof of Glaisher-Crofton Identity |
| title_sort | combinatorics of second derivative graphical proof of glaisher crofton identity |
| url | http://dx.doi.org/10.1155/2018/9575626 |
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